# Question: N balls labeled 1 through N are placed in Box

N balls labeled 1 through N are placed in Box 1 while a Box 2 is initially empty. At each time instant, one of the N balls is chosen (with equally probability) and moved to the other box. Let X [k] be the number of balls in Box 1 at time instant k. Draw a state diagram and find the transition probability matrix for this Markov chain.

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